Never-ending logarithmic series

Algebra Level 2

\[ \log_2x+\log_2\left( \sqrt{x} \right) +\log_2\left(\sqrt{\sqrt{x}}\right)+\log_2\left(\sqrt{\sqrt{\sqrt{x}}}\right)+ \ldots =4\]

What is the positive value of \(x\) that satisfies the equation above?

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